// golden output
gold[0] = 11.9447;
gold[1] = 17.6004;
gold[2] = 18.0517;
gold[3] = 12.4485;
gold[4] = 10.6936;
gold[5] = 11.021;
gold[6] = 19.7199;
gold[7] = 33.8221;
gold[8] = 38.3358;
gold[9] = 35.625;
gold[10] = 33.0517;
gold[11] = 16.116;
gold[12] = 21.4011;
gold[13] = 28.3836;
gold[14] = 32.6059;
gold[15] = 33.8221;
gold[16] = 38.3358;
gold[17] = 28.73;
gold[18] = 18.0412;
gold[19] = 25.7374;
gold[20] = 28.6339;
gold[21] = 28.3836;
gold[22] = 32.6059;
gold[23] = 22.29;
gold[24] = 27.5145;
gold[25] = 35.625;
gold[26] = 33.0517;
gold[27] = 25.7374;
gold[28] = 28.6339;
gold[29] = 22.401;
gold[30] = 15.2995;
gold[31] = 24.5508;
gold[32] = 26.5163;
gold[33] = 24.7961;
gold[34] = 23.7217;
gold[35] = 13.392;
gold[36] = 17.8042;
gold[37] = 23.7794;
gold[38] = 22.0822;
gold[39] = 19.9932;
gold[40] = 18.2539;
gold[41] = 11.77;
gold[42] = 17.8807;
gold[43] = 26.0861;
gold[44] = 32.9287;
gold[45] = 35.3668;
gold[46] = 33.6579;
gold[47] = 21.762;
gold[48] = 18.8157;
gold[49] = 27.3744;
gold[50] = 32.4483;
gold[51] = 26.0861;
gold[52] = 32.9287;
gold[53] = 26.997;
gold[54] = 19.3747;
gold[55] = 31.1951;
gold[56] = 32.4338;
gold[57] = 27.3744;
gold[58] = 32.4483;
gold[59] = 17.657;
gold[60] = 24.0052;
gold[61] = 35.3668;
gold[62] = 33.6579;
gold[63] = 31.1951;
gold[64] = 32.4338;
gold[65] = 21.088;
gold[66] = 10.8142;
gold[67] = 15.2837;
gold[68] = 19.129;
gold[69] = 23.5171;
gold[70] = 26.512;
gold[71] = 17.3371;
